How can I check for collinearity in survey regression? | Stata FAQ

Collinearity is a property of predictor variables and in OLS regression can easily be checked using the
estat vif command after regress or by the user-written command, collin (see How can I use the search command to search for programs and get additional help? for more information about using search). The situation is a little bit trickier when using survey data. We will illustrate this situation using the hsb2 dataset pretending that the variable math is the sampling weight (pweight) and that the sample is stratified on ses. Let’s begin by running a survey regression with socst regressed on read, write and the interaction of read and write. We will create the interaction term, rw, by multiplying read and write together. Since rw is the product of two other predictors, it should create a situation with a high degree of collinearity.

Now, how can we tell if there is high collinearity among the three predictors? To answer this we will run three survey regressions using read, write and rw as the response variables. After each regression we will manually compute the tolerance using the formula 1-R2 and the variance inflation factor (VIF) by 1/tolerance.

Note that we used each of the predictor variables, in turn, as the response variable for a survey regression. VIF values greater than 10 may warrant further examination.

In this example, all of the VIFs were problematic but the variable rw stands out with a VIF of 118.61. The high collinearity of the interaction term is not unexpected and probably is not going to cause a problem for our analysis.

This same approach can be used with survey logit (i.e., svy: logit) or any of the survey estimation procedures. To do this, replace the logit command with the regress command and then proceed as shown above. Running the regress command with a binary outcome variable will not be problem
because collinearity is a property of the predictors, not of the model.